An approach for design optimization of helical gear pair with balanced specific sliding and modified tooth profile

  • Paridhi Rai
  • Asim Gopal BarmanEmail author
Industrial Application


A unique perspective in design optimization of helical gear pair has been emerged and presented in this article. Specific sliding needs to be balanced for enhancing wear and scuffing resistance of helical gears. Optimized modification in tooth profile has immense benefits in gear operations. Effect of profile shift and specific sliding on design optimization of helical gear pair have been studied and found to be beneficial of great importance. Preventing undercutting, balancing of wear and bending fatigue strength and centre distance adjustment are some of the advantages of profile tooth modifications. Real-coded genetic algorithm (RCGA) has been used to attain minimum volume of helical gear pair. Profile shift coefficients for gear and pinion have been included as design variables along with mostly used generic design variables, module, face width and number of teeth on pinion. Specific sliding, transverse contact ratio and face width constraint along with other strength requirements are the design constraints. The optimal design solutions obtained with and without profile shift are recorded and compared with commercially used software for validation. 3D computer-aided design (CAD) models have been developed by using the optimized results obtained from RCGA and commercially used software. These CAD models are used for performing finite element analysis (FEA) on the helical gear set for analyzing the stress developed in the gear pair. The developed stress in the helical gear pair is found to be well within the allowable stress limits for the gear pair.


Helical gear Profile shift Specific sliding Volume optimization Real-coded genetic algorithm FEM analysis 





Pinion tip diameter


Gear tip diameter


Transmission ratio


Tangential load


Application factor


Transverse load factor (bending stress)


Face load factor (bending stress)


Transverse load factor (contact stress)


Face load factor (contact stress)


Dynamic factor


Normal module


Transverse module


Pinion rotational speed


Base diameter




Starting time


Volume of helical gear pair


Pinion profile shift


Gear profile shift


Form factor


Life factor


Stress concentration factor


Helix angle factor


Single pair tooth contact factor (Pinion)


Single pair tooth contact factor(Gear)


Elasticity factor


Zone factor


Lubrication factor


Number of teeth on pinion/gear


Contact ratio factor


Helix angle factor




Nominal permissible bending stress


Nominal permissible contact stress


Allowable bending stress


Allowable contact stress


Transverse pressure angle


Transverse contact ratio








The authors would like to thank Mr. Chinmay Joddar, Manager - Design and Development, New Allenberry Works, Kolkata, India, for helping in validation part with commercially used software.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


  1. Abderazek H, Ferhat D, Atanasovska I, Boualem K (2015) A differential evolution algorithm for tooth profile optimization with respect to balancing specific sliding coefficients of involute cylindrical spur and helical gears. Adv Mech Eng 7(9):1687814015605008CrossRefGoogle Scholar
  2. Abderazek H, Ferhat D, Ivana A (2017) Adaptive mixed differential evolution algorithm for bi-objective tooth profile spur gear optimization. Int J Adv Manuf Technol 90(5-8):2063–2073CrossRefGoogle Scholar
  3. Association AGM (1994) Fundamental rating factors and calculation methods for involute spur and helical gear teeth. American Gear Manufacturers AssociationGoogle Scholar
  4. Chen Z, Zhai W, Shao Y, Wang K (2016) Mesh stiffness evaluation of an internal spur gear pair with tooth profile shift. Sci China Technol Sci 59(9):1328–1339CrossRefGoogle Scholar
  5. Colbourne J (1987) The geometry of involute gears. Springer-Verlag, BerlinCrossRefzbMATHGoogle Scholar
  6. Deb K, Agrawal RB (1994) Simulated binary crossover for continuous search space. Compl Syst 9(3):1–15MathSciNetzbMATHGoogle Scholar
  7. Deb K, Agrawal S (1999) A niched-penalty approach for constraint handling in genetic algorithms. In: Artificial neural nets and genetic algorithms. Springer, pp 235–243Google Scholar
  8. Deb K (2001) Multi-objective optimization using evolutionary algorithms, vol 16. Wiley, New YorkzbMATHGoogle Scholar
  9. Deb K, Deb D (2014) Analysing mutation schemes for real-parameter genetic algorithms. Int J Artif Intell Soft Comput 4(1):1–28MathSciNetCrossRefGoogle Scholar
  10. Diez-Ibarbia A, del Rincon AF, Iglesias M, De-Juan A, Garcia P, Viadero F (2016) Efficiency analysis of spur gears with a shifting profile. Meccanica 51(3):707–723CrossRefGoogle Scholar
  11. Divandari M, Aghdam B, Barzamini R (2012) Tooth profile modification and its effect on spur gear pair vibration in presence of localized tooth defect. J Mech 28(2):373–381CrossRefGoogle Scholar
  12. Dudley DW (1991) Dudley’s gear handbook. Tata McGraw-Hill Education, New YorkGoogle Scholar
  13. Golabi S, Fesharaki JJ, Yazdipoor M (2014) Gear train optimization based on minimum volume/weight design. Mech Mach Theory 73:197–217CrossRefGoogle Scholar
  14. Gologlu C, Zeyveli M (2009) A genetic approach to automate preliminary design of gear drives. Comput Ind Eng 57(3):1043–1051CrossRefGoogle Scholar
  15. ISO 6336 B (2006) Calculation of load capacity of spur and helical gears—. ISO 6336(1):1996Google Scholar
  16. Jelaska D (2012) Gears and gear drives. Wiley, New YorkCrossRefGoogle Scholar
  17. Kumar VS, Muni D, Muthuveerappan G (2008) Optimization of asymmetric spur gear drives to improve the bending load capacity. Mech Mach Theory 43(7):829–858CrossRefzbMATHGoogle Scholar
  18. Maitra G (1994) Handbook of gear design. Tata McGraw-Hill, New YorkGoogle Scholar
  19. Mandol S, Bhattacharjee D, Dan PK (2016) Robust optimization in determining failure criteria of a planetary gear assembly considering fatigue condition. Struct Multidiscip Optim 53(2):291–302CrossRefGoogle Scholar
  20. Mendi F, Baṡkal T, Boran K, Boran FE (2010) Optimization of module, shaft diameter and rolling bearing for spur gear through genetic algorithm. Expert Syst Appl 37(12):8058–8064CrossRefGoogle Scholar
  21. Miler D, Lončar A, Žeželj D, Domitran Z (2017) Influence of profile shift on the spur gear pair optimization. Mech Mach Theory 117:189–197CrossRefGoogle Scholar
  22. Miler D, Žeželj D, Lončar A, Vučković K (2018) Multi-objective spur gear pair optimization focused on volume and efficiency. Mechanism and Machine TheoryGoogle Scholar
  23. Pedrero J, Artés M (1996) Approximate equation for the addendum modification factors for tooth gears with balanced specific sliding. Mech Mach Theory 31(7):925–935CrossRefGoogle Scholar
  24. Rai P, Barman AG (2018) Design optimization of spur gear using sa and RCGA. J Braz Soc Mech Sci Eng 40:1–8CrossRefGoogle Scholar
  25. Rai P, Agrawal A, Saini ML, Jodder C, Barman AG (2018) Volume optimization of helical gear with profile shift using real coded genetic algorithm. Procedia Comput Sci 133:718–724CrossRefGoogle Scholar
  26. Salomon S, Avigad G, Purshouse RC, Fleming PJ (2016) Gearbox design for uncertain load requirements using active robust optimization. Eng Optim 48(4):652–671MathSciNetCrossRefGoogle Scholar
  27. Savsani V, Rao R, Vakharia D (2010) Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mech Mach Theory 45(3):531–541CrossRefzbMATHGoogle Scholar
  28. Tudose L, Buiga O, Ṡtefanache C, Sóbester A (2010) Automated optimal design of a two-stage helical gear reducer. Struct Multidiscip Optim 42(3):429–435CrossRefGoogle Scholar
  29. Van Thoan P, Wen G, Yin H, Van Sy N (2015) Choosing the optimal addendum modification coefficient of external involute spur gear. Aust J Mech Eng 13(3):145–153CrossRefGoogle Scholar
  30. Wan Z, Zhang S (2013) Formulation for an optimal design problem of spur gear drive and its global optimization. Proc Instit Mech Eng Part C: J Mech Eng Sci 227(8):1804–1817CrossRefGoogle Scholar
  31. Yokota T, Taguchi T, Gen M (1998) A solution method for optimal weight design problem of the gear using genetic algorithms. Comput Ind Eng 35(3-4):523–526CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Institute of Technology PatnaPatnaIndia

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